What is factor (7z^3-xy)^4-9 ?

The solution to factor (7z^3-xy)^4-9 is (49z^6-14z^3xy+x^2y^2+3)(49z^6-14z^3xy+x^2y^2-3)

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factor (7z^3-xy)^4-9

factor

(7 z^{3} - x y)^{4} - 9

(49 z^{6} - 14 z^{3} x y + x^{2} y^{2} + 3) (49 z^{6} - 14 z^{3} x y + x^{2} y^{2} - 3)

Solution steps

(7 z^{3} - x y)^{4} - 9

(7 z^{3} - x y)^{4} = ((7 z^{3} - x y)^{2})^{2}

9 = 3^{2}

= ((7 z^{3} - x y)^{2})^{2} - 3^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

((7 z^{3} - x y)^{2})^{2} - 3^{2} = ((7 z^{3} - x y)^{2} + 3) ((7 z^{3} - x y)^{2} - 3)

= ((7 z^{3} - x y)^{2} + 3) ((7 z^{3} - x y)^{2} - 3)

Simplify

((7 z^{3} - x y)^{2} + 3) ((7 z^{3} - x y)^{2} - 3) : (49 z^{6} - 14 z^{3} x y + x^{2} y^{2} + 3) (49 z^{6} - 14 z^{3} x y + x^{2} y^{2} - 3)

= (49 z^{6} - 14 z^{3} x y + x^{2} y^{2} + 3) (49 z^{6} - 14 z^{3} x y + x^{2} y^{2} - 3)

(2 x + \frac{1}{2})^{2}

\frac{( x ^{6} - 1 )}{( x - 1 )}

\frac{12}{99}

85 + 115

\frac{1}{- 2 ^{2}}

What is factor (7z^3-xy)^4-9 ?
The solution to factor (7z^3-xy)^4-9 is (49z^6-14z^3xy+x^2y^2+3)(49z^6-14z^3xy+x^2y^2-3)